Linked Questions

4 votes
0 answers
523 views

The interaction picture doesn't exist? [duplicate]

I have recently encountered Haag's theorem and according to Wikipedia: Rudolf Haag postulated [1] that the interaction picture does not exist in an interacting, relativistic quantum field theory (...
Jack's user avatar
  • 991
63 votes
7 answers
16k views

Rigor in quantum field theory

Quantum field theory is a broad subject and has the reputation of using methods which are mathematically desiring. For example working with and subtracting infinities or the use of path integrals, ...
MBN's user avatar
  • 3,775
33 votes
2 answers
10k views

The concept of particle in QFT

I never learnt QFT and I apologize for my (probably) elementary question. Somebody told me that in QFT a particle is viewed as an irregularity in the field. On the other hand, in an article in ...
Sofia's user avatar
  • 6,806
16 votes
1 answer
4k views

When we define the S-matrix, what are "in" and "out" states?

I have seen the scattering matrix defined using initial ("in") and final ("out") eigenstates of the free hamiltonian, with $$\left| \vec{p}_1 \cdots \vec{p}_n \; \text{out} \right\rangle = S^{-1} \...
A. Zerkof's user avatar
  • 163
10 votes
2 answers
906 views

Can we always express the EM-Field Hamiltonian as (possibly time dependent) pair of annihilation and creation operators?

The EM-Field Hamiltonian is, in principle, a functional (with a chosen operator ordering) that is defined on operator-fields $\hat{A}(x)$ and $\partial_\mu \hat{A}$. If you carry out the calculations ...
Quantumwhisp's user avatar
  • 6,693
11 votes
1 answer
2k views

Fock space vs. wavefunctionals

There are at least two representations of the Hilbert spaces of quantum field theory. For a scalar field, we have The Fock space representation, such that every state is represented as the Fock ...
Slereah's user avatar
  • 16.1k
6 votes
1 answer
804 views

Does Haags Theorem forbid Time-Evolution?

I didn't quite grasp the essence of Haags Theorem in the the way it is presented (for example on wikipedia), but the issue seems to be that if one wants to represent infinitely degrees of freedom ...
Quantumwhisp's user avatar
  • 6,693
1 vote
2 answers
394 views

Does the fact that we cannot exactly solve the Standard Model undermine the validity of QFT?

I have seen discusstions of this types before: there is a question about photons or virtual particles or vaccuum, etc. And there is usually a good and clear explanation from the point of view of ...
Tziolkovski's user avatar
6 votes
2 answers
1k views

Ground state for interacting field thoeries

Are there references where the ground state of an interacting quantum field theory is explicitly written in terms of states of the underlying free theory? For example, let us suppose to have a self ...
Yesterday's user avatar
6 votes
1 answer
307 views

In what way do non-rigorous arguments make sense? [closed]

I specifically have in mind arguments made in QFT textbooks in mind. There are no rigorous foundations for QFT, at least not any that can reproduce the predictions of the Standard Model. In fact, ...
Physical Mathematics's user avatar
7 votes
1 answer
790 views

A question about the energy of turning on and off interaction adiabatically in QFT

I read a saying as follows: In a theory with no particles which decay and no bound states, the turning on and off of the interactions merely serves to limit the effective range of forces. In this ...
346699's user avatar
  • 5,881
4 votes
1 answer
203 views

Is unphysical states still unphysical in an interaction theory?

Maggiore A modern introduction to quantum field theory Section 4 : In free quantum electromagnetic field theory... since only the two degree of freedom transverse wave, the energy, and the momentum, ...
ShoutOutAndCalculate's user avatar